Here are what are sometimes called the "CLASSIC functions", because
each starts with a letter of the word "CLASSIC". 

C is for the CUBING function.          y = x³
L is for the LINEAR functions.         y = mx + b
A is for the ABSOLUTE VALUE function   y = |x|
S is for the SQUARING finction         y = x²
S is for the SQUARE ROOT function      y = 
I is for the IDENTITY function         y = x
C is for the CUBE ROOT function        y =  

All CLASSIC functions except the LINEAR function go through 
(0,0) and (1,1).  Some also go through (-1,1), and some go 
through (-1,-1).

The CUBING function y = x³ looks like this  It also goes through (1,-1)
The LINEAR function y = mx+b can represent any line with slope m and y-intercept (0,b)
The ABSOLUTE VALUE function y = |x| looks like this  It also goes through (-1,1)
The SQUARING function y = x² looks like this  It also goes through (-1,1)
The SQUARE ROOT function y =  looks like this  It goes thru (1,1) but stops at the origin.
The IDENTITY function y = x looks like this  It also goes through (-1,-1)
The CUBE ROOT function y =  looks like this  It also goes through (-1,1)

All the CLASSIC functions except the linear function necessarily go through
(0,0) and (1,1).

Edwin